28278 + Interview Questions in Maths in Class 12

1.	The solution of x(dy)/(dx) + 2y = x^(2) log x is
Answer» `YX^(2) = (x^(4))/(4)LOG x - (x^(4))/(16) + c` `yx^(2) = (x^(4))/(4)log x + (x^(4))/(16) + c` `XY^(2) = (x^(4))/(4)log x - (x^(4))/(16) + c` `xy^(2) = (x^(4))/(4)log x - (x^(4))/(6) + c` Answer :A

Discussion

2.	Passage 1 The second section gives power to the President, "by and with the advice and consent of the Senate, to make treaties, provided two thirds of the Senators present concur…" Some are displleased with it, not on account of any errors or defects in it, but because they say the treaties will have the force of laws, and thus should be made only by the legislature. These gentlemen seem not to consider that the judgement of our courts, and the commissions constitutionally given by our governor, are as valid and as binding on all persons whom they concern as the laws passed by our legislature. All constitutional acts of power, whether in the executive or in the judicial department, have as much legal validity and obligation as if they proceeded from the legislature. it surely does not follow that because the people have given the power of makin laws to the legislature, they should therefore likewise give the legislature the power to do every other act of government by which the citizens are to the bound and affected. The President is to have power, "by and with the advice and consent of the Senate, to make treaties, provided two thirds of the senators present concur."... Though several writers o teh subject of government place the power of making treatis in the class of executive aunthorities, this is evidently an arbitrary classicication, for if we attend carefully to its operation, it will be found to partake more of the legislative than of the executive character, though it does not seem strictly to fall within the definition of either of them. The essence of teh legislative branch is to enact laws, or, in other words, to prescribe rules for the regulation of teh society, while the execution of the laws, and the employment of the common strength, either for this purpose of for the common defense, seem to comprise all the functions of the executive branch. The power of making treaties is, plainly, neither the one nor the other. It relates neither to the execution of the existing laws, nor to the creation of new ones, and still less to an exertion of the common strength. Its objects are CONTRACTS with foreign nations, which have the force of law, but derive it from the obligations of good faith. They are not rules prescribed by the government of the citizen, but agreements between two governments. The power in questin seems therefore to form a distinct department, and to belong, properly, neither to the legislative nor to the exective branch. The qualties elsewhere detailed as indispensable in the management of foreign negotiations point to the Exective as the best agent in those transactions, while the vast importance of the trust, and the operation of treaties as laws, plead strongly for the participation of the whole or a portion of the legislative body in the office of making them. Based on Passage 2, it can be inferred that Hamilton would agree with which of the following statements ?
Answer» Most writers on the subject of government fail to PROVIDE evidence suffcient to SUPPORT their conslusions. CITIZENS should not be bound by agreements between one government and another. Any POWER that is not properly described as judicial or legislative must be an executive power. At least some writers on the subject of government reach unsubstantiated conclusions about the scope of exective authority. ANSWER :D

Discussion

3.	P(-9,-1) is a point on the circle x^2+y^(2)+4x+8y-38=0. The equation to the tangent at the other end of the diameter thorugh P is
Answer» `7x-3y=60` `7x+3y=56` `7x-3y=56` `7x+3y=60` ANSWER :C

Discussion

4.	If x ge 0, y ge 0, 2 le x+y le 8, 2+y le 10 then the maximum value of F=5x+7y is
Answer» 14 25 52 56 Answer :D

Discussion

5.	Evaluate the following integrals. int(2cosx+3sinx)/(4cosx+5sinx)dx
Answer» ANSWER :`(23)/(41)X-(2)/(41)log\|4cosx+5sinx\|+c`

Discussion

6.	If the graph of a differentiable function y = f(x) meets the lines y = -1 and y = 1, then the graph :
Answer» does not MEET the line y = 0 meets the line y = 0 ATLEAST thrice meets the line y = 0 atleast TWICE meets the line y = 0 at LEAST once. Answer :D

Discussion

7.	If a and b are complementary angles (they sun to 90^(@)), name three other pairs of complementry angles .
Answer» ANSWER :B and d, a and E, & d and e

Discussion

8.	Find the number of terms in the expansion of (x + 2y)^20 + (x - 2y)^20
Answer» ANSWER :11

Discussion

9.	The value of cot^(2)""(pi)/(7)+cot^(2)""(2pi)/(7)+cot^(2)""(3pi)/(7), is
Answer» 0 5 9 `1//3` ANSWER :B

Discussion

10.	If P(A)=0.8, P(B)=0.5 and P(B\|A)=0.4, find (i) P(A cap B) (ii)P(A\|B) (iii) P(A cup B)
Answer» ANSWER :(i) 0.32 (II) 0.64 (III) 0.98

Discussion

11.	Circles with radii 3,4,5 are touching each other externally , If P is the point of intersection of tangents to these circles at their point of contact ,the distances of P from the points of contact is
Answer» `SQRT2` ` SQRT5` ` 4` `sqrt7` ANSWER :B

Discussion

12.	If A + B = C, where A and B are matrices of order 2 xx 3, then order of C is :
Answer» 32 23 22 33 Answer :B

Discussion

13.	C_1 - C_3 + C_5 - C_7 + …...
Answer» `2^(n-1)` `2^(n//2) SIN ((NPI)/(4))` `2^(n//2) cos ((npi)/(4))` 0 Answer :B

Discussion

14.	LetA (z_1 )andB(z_2 )be lying onthe curve\|z-3 - 4i\| = 5, where\|z_1 \|is maximum. Now,A(z_1) is rotated about the origin inanticlockwise direction through 90^(@)reachingatP(z_0). IfA, B and Pare collinear thenthevalue of(\|z_0 - z_ 1 \| * \|z_ 0- z_ 2 \|)is _______.
Answer» SOLUTION :We have `\|z-(3+4i)\| = 5` So, z lies on the circlehaving centre at `3+4i` and radius 5. This circlepasses thorughtthe origin. `z_(1)` lies on circlesuch that `\|z_(1)\|` is MAXIMUM. Therefore ,`z_(1) ` is at other end of thediameter through origin. `therefore z_(1) = 6+ 8i` OAis rotated by `90^(@)` in anticlcokwise DIRECTION. So, `z_(0) = i(6+8i) = - 8+ 6i` Since A,B and P are colliner. `\|z_(0)-z_(1)\|.\|z_(0)-z_(2)\| = Pa.PB =OP^(2) = 10^(2) = 100`

Discussion

15.	Find the derivative of (2x+3)/(x-2) from first principle.
Answer» ANSWER :`(-7)/((x-2)^(2))`.

Discussion

16.	int cosec^5 x dx =
Answer» `(cosec X cot^3 x )/(4) - 5/8 cosec x cot x + 3/8 LOG \| tanx/2 \| + c ` `- (cosec x cot^3 x )/(4) - 5/8 cosec x cot x + 3/8 log \| TAN x/2 \| + c ` ` - (cosecc^3 x cot x )/(4) - 3/8 cosec x COTX + 3/8 log \| tan x/2 \| + c` `- (cosec^3 x cot x )/(4) + 3/8 cosec x cotx - 3/8 log \| tan x/2 \| + c ` Answer :C

Discussion

17.	Evaluate the following integrals. intcos^(3)xsinxdx
Answer» ANSWER :`-(1)/(4)COS^(4)x+c`

Discussion

18.	((cos15^(@)-sin15^(@)+1)/(cos15^(@)+sin15^(@)+1))((1+sin15^(@))/(cos15^(@)))
Answer» `2-sqrt(3)` 1 `2+sqrt(3)` NONE of these Answer :A

Discussion

19.	If sin x + sin y= (1)/(2) and cos x + cos y=1, then tan (x+y) =______
Answer» `(4)/(3)` `(-8)/(3)` `-(3)/(4)` `(8)/(3)` ANSWER :A

Discussion

20.	Find the area of the region bounded by y=f(x),y=\|g(x)\| and the lines x=0,x=2, where f,g are continuous function satisfying f(x+y)=f(x)+f(y)-8xy,AA x, y in R and g(x+y)=g(x)+g(y)+3xy(x+y),AA x,y in R also , f'(0)=8 and g'(0)=-4.
Answer» ANSWER :`4/3` SQ UNITS

Discussion

21.	** is a binary operation on the set Q. a""b=a+12b+abthen find 2""(1)/3
Answer» SOLUTION :N/A

Discussion

22.	Find (dy)/(dx)," if "sin^(2)x + cos^(2)y= k, where k is constant.
Answer» ANSWER :`(SIN 2X)/(sin 2Y)`

Discussion

23.	(vec(a).hat(i))^(2)+(vec(a).hat(j))^(2)+(vec(a).hat(k))^(2)=
Answer» `\|VEC(a)\|^(2)` `2\|vec(a)\|^(2)` `3\|vec(a)\|^(2)` `4\|vec(a)\|^(2)` ANSWER :A

Discussion

24.	Some events related to a capacitor are listed in column-I Match these events with their effect (s) is column-II {:(,"Column-I",,"Column-II"),("(A)","Insertion of dielectric while battery remain attached",,"(P)Electric field between plates changes"),("(B)","Removal of dielectric while battery is not present",,"(Q)Charge present on plates changes"),("(C)","Slow decrease in separation between plates while battery is attached",,"(R)Energy stored in capacitor increases"),("(D)","Slow increase of separation between plates while battery is not present",,"(S)Work done by external agent is positive"):}'
Answer» Solution :(A) when battory is connectedthen on INSERTION of DIELECTRIC - charge becomes K time and ALSO energy becomes k time while case of battery is not present then charge remain conserved (B) with in case in seperation CAPACITANCE decrease

Discussion

25.	In a class 30% of the student fail in Mathematics,20% of the student fail in English and 10% fail in both.If he has failed in English, what is the probability thet he has failed in Mathematics?
Answer» SOLUTION :If he has FAILED in English, then the probaility that he has failed in Mathematics `i.e.,P(A/B)=P((ACAPB))/(P(B))=(10/100)/(20/100)=1/2`

Discussion

26.	Solve by Cramer's rule : ax+by+cz=1, cx+ay+bz=0, bx+cy+az=0, given that, A,B,C are the cofactors of the elemets a,b,c in D where D=a\|{:(a,b,c),(c,a,b),(b,c,a):}\|
Answer» ANSWER :`(A)/(D),(B)/(D),(C )/(D)`

Discussion

27.	The vertices of the feasible region determined by some linear constraints are (0,2), (1,1),(3,3), (1,5). Let Z=px + qy where p,q gt 0. The condition on p and q so that the maximum of Z occurs at both the points (3, 3) and (1, 5) is .......
Answer» `p=q` `p=2q` `q=2p` `p=3q` ANSWER :A

Discussion

28.	If A=[[1,2],[-2,3]]B=[[3,2],[1,4]],C=[[2,2],[1,3]]Calculate AC.
Answer» SOLUTION :`AC=[[1,2],[3,4]][[2,2],[1,3]]` `=[[1.2+2.1""1.2+2.3],[3.2+4.1" "3.2+4.3]]=[[4,8],[10,18]]`

Discussion

29.	x^(2) log x
Answer» Solution :` INT x^(2) LOGX DX` ` = LOG x. INTX^(2) dx- int {(d)/(dx) log x. int x^(2) dx}dx` (Takinglog x asfirstfucntion) ` = log x. (x^(2))/(3)- int (1)/(x).(x^(3))/(3) dx +C` ` =(x^(3))/(3) log x. (1)/(3).int x^(2) dx +C` ` =(x^(3))/(3) log x -(1)/(3).(x^(3))/(3)+C` ` =(x^(3))/(3) log x -(x^(3))/(9)+C`

Discussion

30.	A tangent to the ellipse (x^(2))/(4)+(y^(2))/(1)=1 cuts the circle x^(2)+y^(2)=4 at point A and B C is any point on the circle x^(2)+y^(4)=4 such that A, B and C are to the same side of x-axis find the maximum , area of the traingle ABC.
Answer» ANSWER :`SQRT(3)`

Discussion

31.	Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r), then Q. The value of underset(0 le r lt s le n)(sum sum)(C_(r)+-C_(S))^(2) is
Answer» `(N UNDERSET(+)(-)1).^(2n)C_(n)+-2^(2n)` `(n+1).^(2n)C_(n)+2^(2n-1)` `(n+-1).^(2n)C_(n)+-2^(2n)` `(n+1).^(2n)C_(n)-2^(2n-1)` Answer :A

Discussion

32.	The vector vecc. (vecb+vecc) xx (veca +vecb+vecc) is equal to
Answer» `VECC. Vecb xx VECA` 0 `vecc. Veca xx vecb` `veca. Vecc xx vecb` Answer :A

Discussion

33.	Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r), then Q. The values of underset(r=0)overset(n)(sum)underset(s=0)overset(n)(sum)(C_(r)+C_(S)) is
Answer» `(N+1)2^(n+1)` `n.2^(n)` `(n+1)2^(n)` `n.2^(n-1)` ANSWER :A

Discussion

34.	Ifalpha=(5)/(2!3!) + (5.7)/(3!3^2)+ (5.7.9)/(4!3^3) +…,thenalpha ^ 2 + 4 alphaisequalto
Answer» 21 23 25 27 Solution :GIVENTHAT `alpha= (5 ) /(2!3 )+(5.7 )/(3!3^ 2 )+ (5.7.9)/(4!3^3) +… ` ` (1 + X ) ^n= 1 + (NX )/(1 !)+(n(n - 1 ))/(2!)x ^ 2+(n (n-1) (n - 2 ))/(3!) x ^3` `+ (n(n - 1 )(n - 2 ) (n - 3 ))/(4!)x ^4 + ... "" ` ...(2) On comparingthe termsofabovetwoexpansions, weget, ` (n(n - 1))/(2!)x ^ 2 =(5 )/(2!3)"" `...(1) `(n(n - 1)(n - 2))/(3 ! ) x ^ 3=(5.7 ) /(3 ! 3^ 2 ) "" `...(2) ` (n (n - 1 )(n - 2 )(n - 3 ))/(4 ! )x ^ 4 =(5.7.9)/(4!3^3) "" `...(3) `(2)div (1) ,(3) div (2)` `(n - 2 )x = (7 ) /(3) "" `...(4) ` (n - 3 )x=3 ""`... (5) ` (7)/(3x)- (3 )/(x)=1 "" ` [From(4)and(5) ] `(-2 ) /(3x )=1 ` ` rArrx =(-2)/(3 ) ` `RARR(n - 2 )(( -3 )/(2)) =(7)/(2)` ` rArrn = 2- (7)/(2)` `rArr n =(-3)/(2) ` `therefore(1 -(2)/(3))^(-3/2)= 1 +((-3/2) (-2/3))/(1!)+((-3/2)(-3/2) - (1)/(2!) (-2/3)^2 +... ` [`because` From (2) ] `rArr(1 - (2)/(3)) ^(-3/2) = 1+ 1 + (5 )/(2!3) +(5.7 ) /(3!3^2)+... ` ` rArr3^(3//2)= 2+(5)/(2!3)+(5.7 ) / (3 !3 ^ 2 )+ ... ` `3 ^(3//2)=2+alpha` `rArr (5 ) /2 ! 3 )+(5.7 ) /( 3 ! 3 ^ 2 )+...=3 ` `thereforealpha=3 ^(3//2 ) - 2` `alpha + 2=3 ^(3//2 ) ` ` rArr (alpha+2 ) ^2=3 ^ 2 ` `rArralpha ^ 2+4 alpha=27 - 4` `rArralpha ^ 2+ 4 alpha=23 `

Discussion

35.	If omega is a complex cube root of unity , thenthe value of (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) + (a + b omega + comega^(2))/(b + c omega + a omega^(2)) is
Answer» 0 `-1` 1 2 Answer :B

Discussion

36.	Number of normal(s) that can be drwan through the point (sqrt(2,2)) to the ellipse (x^(2))/(2)+(y^(2))/(1)=1 is / are
Answer» 0 1 2 More than 2 Solution :`T=S_(1)rarr3rarr3xh-2yk+2(x+h)-3(y+k)=3h^(2)-2k^(2)+4h-6k` SLOPE `=2implies(-3h-2)/(-2k-3)=2implies-3n-2=-4y-6implies3n-4y=14`

Discussion

37.	A diagonal matrix is said to be a ____________ if its diagonal elements are equal (other than unity).
Answer» ANSWER :SCALAR MATRIX.

Discussion

38.	Which of the following is correct order of acidic strength ?
Answer» LIOH LT NAOH lt KOH BeO lt MGO lt CAO `Al_2O_3 lt SiO_2 lt P_2O_5` `H_2S lt H_2O`

Discussion

39.	If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x, then the coefficient of x^(3) is
Answer» `(-73)/648` `73/648` `71/648` `(-71)/648` ANSWER :A

Discussion

40.	If the focii of the ellipse x^(2)/25+y^(2)/(16)=1 and the hyperbola x^(2)/4-y^(2)/b^(2)=1 coincide, then b^(2) is equal to
Answer» 4 5 8 9 Answer :B

Discussion

41.	A train covers the first half of the distance between two stations with a speed of 40 km/h and the other half with 60 km/h. Then its average speed is :
Answer» 50 km/h 48 km/h 52 km/h 100 km/h Answer :A

Discussion

42.	The solution of (dy)/(dx) = (x + 7y + 2)/(3x + 5y + 6) is
Answer» `(y + X + 2)^(4) = c (x + 5Y + 2)` `(y -x 02)^(4) = c (x-5y -2)` `(y-x-2)^(4) = c (x + 5y + 2)` `(y -x-2)^(4) = c (x-5y -2)` ANSWER :C

Discussion

43.	The probability distribution of a random variable X is given as under : P(X=x)={(kx^(2)",",x="1, 2, 3"),(2kx",",x="4,5,6"),(0"", "Otherwise"):} where k is a constant. Calculate (i) E(X), (ii) E(3X^(2)) and (iii) P(x ge 4).
Answer» ANSWER :`(i) 4.32, (II) 61.92, (III) (15)/(22)`

Discussion

44.	If the direction cosines of bar(AB) are (-2)/(sqrt(17)), (3)/(sqrt(17)), (-2)/(sqrt(17)) such that A-=(3, -6, 10) and l(AB)=sqrt(17), then the co-ordinates of point B are
Answer» (1, 3, -8) or (5, -9, 12) (1, -3, 8) or (5, -9, 12) (1, -3, 8) or (5, 9, -12) (1, 3, -8) or (5, 9, -12) ANSWER :B

Discussion

45.	If Q is an ..............
Answer» SOLUTION :

Discussion

46.	Two balanced dice are tossed 500 times. If sum of integersobtained on dice is 9 will be the success then …….and ……….are the mean and variance of success.
Answer» `(500)/(9) and (4000)/(81)` `(1)/(9) and (8)/(9)` `(4000)/(81) and (500)/(9)` `(500)/(9) and (4000)/(9)` ANSWER :A

Discussion

47.	Mean and variance of variable X of the binomial distribution are (7)/(3) and (14)/(9) . Then ………… is the probability for X = 6 or 7.
Answer» `(1)/(729)` `(5)/(729)` `(7)/(729)` `(13)/(729)` Answer :B

Discussion

48.	A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/sec. At that instant, when the radius of circular wave is 8 cm, how fast is the enclosed area is increasing
Answer» `6PI cm^(2)//s` `8 PI cm^(2)//s` `(8)/(3) cm^(2)//s` `80 pi cm^(2)//s` ANSWER :D

Discussion

49.	sin21^(@)cos9^(@)-cos84^(@) cos6^(@)=
Answer» `1//4` `1//8` `3//2` `3//8` ANSWER :A

Discussion

50.	Letvec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i)+ hat(j) + hat(k),vec(c) = 3hat(i) + 2hat(j) + hat(k) and vec(d) = 3hat(i) - hat(j) - 2hat(k), then . Find the value of (vec(a) xx vec(b)) xx (vec(a) xx vec(b)).vec(d)
Answer» ANSWER :`-100`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The solution of x(dy)/(dx) + 2y = x^(2) log x is

P(-9,-1) is a point on the circle x^2+y^(2)+4x+8y-38=0. The equation to the tangent at the other end of the diameter thorugh P is

If x ge 0, y ge 0, 2 le x+y le 8, 2+y le 10 then the maximum value of F=5x+7y is

Evaluate the following integrals. int(2cosx+3sinx)/(4cosx+5sinx)dx

If the graph of a differentiable function y = f(x) meets the lines y = -1 and y = 1, then the graph :

If a and b are complementary angles (they sun to 90^(@)), name three other pairs of complementry angles .

Find the number of terms in the expansion of (x + 2y)^20 + (x - 2y)^20

The value of cot^(2)""(pi)/(7)+cot^(2)""(2pi)/(7)+cot^(2)""(3pi)/(7), is

If P(A)=0.8, P(B)=0.5 and P(B|A)=0.4, find (i) P(A cap B) (ii)P(A|B) (iii) P(A cup B)

Circles with radii 3,4,5 are touching each other externally , If P is the point of intersection of tangents to these circles at their point of contact ,the distances of P from the points of contact is

If A + B = C, where A and B are matrices of order 2 xx 3, then order of C is :

C_1 - C_3 + C_5 - C_7 + …...

LetA (z_1 )andB(z_2 )be lying onthe curve|z-3 - 4i| = 5, where|z_1 |is maximum. Now,A(z_1) is rotated about the origin inanticlockwise direction through 90^(@)reachingatP(z_0). IfA, B and Pare collinear thenthevalue of(|z_0 - z_ 1 | * |z_ 0- z_ 2 |)is _______.

Find the derivative of (2x+3)/(x-2) from first principle.

int cosec^5 x dx =

Evaluate the following integrals. intcos^(3)xsinxdx

((cos15^(@)-sin15^(@)+1)/(cos15^(@)+sin15^(@)+1))((1+sin15^(@))/(cos15^(@)))

If sin x + sin y= (1)/(2) and cos x + cos y=1, then tan (x+y) =______

Find the area of the region bounded by y=f(x),y=|g(x)| and the lines x=0,x=2, where f,g are continuous function satisfying f(x+y)=f(x)+f(y)-8xy,AA x, y in R and g(x+y)=g(x)+g(y)+3xy(x+y),AA x,y in R also , f'(0)=8 and g'(0)=-4.

** is a binary operation on the set Q. a"*"b=a+12b+abthen find 2"*"(1)/3

Find (dy)/(dx)," if "sin^(2)x + cos^(2)y= k, where k is constant.

(vec(a).hat(i))^(2)+(vec(a).hat(j))^(2)+(vec(a).hat(k))^(2)=

In a class 30% of the student fail in Mathematics,20% of the student fail in English and 10% fail in both.If he has failed in English, what is the probability thet he has failed in Mathematics?

Solve by Cramer's rule : ax+by+cz=1, cx+ay+bz=0, bx+cy+az=0, given that, A,B,C are the cofactors of the elemets a,b,c in D where D=a|{:(a,b,c),(c,a,b),(b,c,a):}|

The vertices of the feasible region determined by some linear constraints are (0,2), (1,1),(3,3), (1,5). Let Z=px + qy where p,q gt 0. The condition on p and q so that the maximum of Z occurs at both the points (3, 3) and (1, 5) is .......

If A=[[1,2],[-2,3]]B=[[3,2],[1,4]],C=[[2,2],[1,3]]Calculate AC.

x^(2) log x

A tangent to the ellipse (x^(2))/(4)+(y^(2))/(1)=1 cuts the circle x^(2)+y^(2)=4 at point A and B C is any point on the circle x^(2)+y^(4)=4 such that A, B and C are to the same side of x-axis find the maximum , area of the traingle ABC.

Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r), then Q. The value of underset(0 le r lt s le n)(sum sum)(C_(r)+-C_(S))^(2) is

The vector vecc. (vecb+vecc) xx (veca +vecb+vecc) is equal to

Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r), then Q. The values of underset(r=0)overset(n)(sum)underset(s=0)overset(n)(sum)(C_(r)+C_(S)) is

Ifalpha=(5)/(2!3!) + (5.7)/(3!3^2)+ (5.7.9)/(4!3^3) +…,thenalpha ^ 2 + 4 alphaisequalto

If omega is a complex cube root of unity , thenthe value of (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) + (a + b omega + comega^(2))/(b + c omega + a omega^(2)) is

Number of normal(s) that can be drwan through the point (sqrt(2,2)) to the ellipse (x^(2))/(2)+(y^(2))/(1)=1 is / are

A diagonal matrix is said to be a ____________ if its diagonal elements are equal (other than unity).

Which of the following is correct order of acidic strength ?

If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x, then the coefficient of x^(3) is

If the focii of the ellipse x^(2)/25+y^(2)/(16)=1 and the hyperbola x^(2)/4-y^(2)/b^(2)=1 coincide, then b^(2) is equal to

A train covers the first half of the distance between two stations with a speed of 40 km/h and the other half with 60 km/h. Then its average speed is :

The solution of (dy)/(dx) = (x + 7y + 2)/(3x + 5y + 6) is

The probability distribution of a random variable X is given as under : P(X=x)={(kx^(2)",",x="1, 2, 3"),(2kx",",x="4,5,6"),(0"", "Otherwise"):} where k is a constant. Calculate (i) E(X), (ii) E(3X^(2)) and (iii) P(x ge 4).

If the direction cosines of bar(AB) are (-2)/(sqrt(17)), (3)/(sqrt(17)), (-2)/(sqrt(17)) such that A-=(3, -6, 10) and l(AB)=sqrt(17), then the co-ordinates of point B are

If Q is an ..............

Two balanced dice are tossed 500 times. If sum of integersobtained on dice is 9 will be the success then …….and ……….are the mean and variance of success.

Mean and variance of variable X of the binomial distribution are (7)/(3) and (14)/(9) . Then ………… is the probability for X = 6 or 7.

A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/sec. At that instant, when the radius of circular wave is 8 cm, how fast is the enclosed area is increasing

sin21^(@)cos9^(@)-cos84^(@) cos6^(@)=

Letvec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i)+ hat(j) + hat(k),vec(c) = 3hat(i) + 2hat(j) + hat(k) and vec(d) = 3hat(i) - hat(j) - 2hat(k), then . Find the value of (vec(a) xx vec(b)) xx (vec(a) xx vec(b)).vec(d)

** is a binary operation on the set Q. a""b=a+12b+abthen find 2""(1)/3